Some technical measuring tasks yield several phase measurement values; the quantity to be measured, e.g. an angle or a distance to a target, must be determined from among these phase measurement values.
Examples of this include:
Distance measurement with RADAR or with modulated laser light. N measurements are carried out with different frequencies f1 . . . fN. At the reception point, the signals reflected by the target at a distance of x have the following phase shifts (c=the speed of light):       α    i    =            2      ·      π      ·              f        i            ·      2      ·      x        c  
The phase shifts are thus proportional to the quantity to be measured and to the frequency used. However, the actual measurement values of the phases always lie in the range from 0 to 2xcfx80, i.e. they are always determined only up to integral multiples of 2xcfx80.
Optical angle transmitter: scanning of N optical ruled gratings. N traces are placed on a disk or a cylinder with optical ruled gratings. In one rotation, there are therefore ni periods or marks. If the phase positions of the traces are measured with the aid of optoelectronic detectors in relation to a fixed measurement window, then this yields the phase positions:
xe2x80x83xcex1=nixc2x7xcfx86
The phases are thus proportional to the torsion angle xcfx86 and the periodicities ni. Here, too, the actual measurement values always lie in the range from 0 to 2xcfx80.
The following methods are known for evaluating these signals, i.e. for determining x and xcfx86:
Classic Vernier Method:
The difference between 2 measurement angles is calculated; if it is less than 0, then 2xcfx80 is added. This method has serious limitations: measurement errors in the angles have a significant impact on the end result; in addition, the method only works if the two periodicities being considered differ by precisely 1.
Modified Vernier Method (See DE P 19506938):
From 2 measurement angles, the value of the quantity to be measured is determined through weighted addition and the further addition of an angular range-dependent constant. The advantage therein is that measurement errors in the angles are reduced by a factor of  less than 1.
Cascaded, Modified Vernier Method:
The modified vernier method is used multiply for a number of traces in a hierarchical arrangement.
The object of the invention is to obtain an optimal, unambiguous phase measurement value from N multivalued, distorted phase signals xcex1i, wherein the disadvantages of the known methods are circumvented.
Possible uses include tasks in which a high-precision, robust measurement value must be determined from among a number of phase signals, e.g.:
multi-frequency distance measurement
angle measurement
combined angle- and torque measurement
using RADAR, laser, optical, magnetic, or other sensor principles.
The invention permits direct, optimal, non-hierarchical evaluation of N phase signals.
In contrast with the known methods, virtually any periodicity ni can be used. Measurement errors in the individual phase signals are clearly reduced. The inclusion of a number of phase traces can achieve a distinctly increased tolerance with regard to measurement errors.
In particular, the invention is suited to optimally evaluating the signals of an optical TAS (torque angle sensor).